Supercharacters and pattern subgroups in the upper triangular groups

2010/08/13 by Le, Tung
#20C15 #20C33 #20D15 #20D20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1008.2269

Abstract

Let U_n(q) denote the upper triangular group of degree n over the finite field \F_q with q elements. It is known that irreducible constituents of supercharacters partition the set of all irreducible characters \Irr(U_n(q)). In this paper we present a correspondence between supercharacters and pattern subgroups of the form U_k(q)∩ ^wU_k(q) where w is a monomial matrix in GL_k(q) for some k

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